Yes you can use BA avios for award flights on any oneworld or BA partner, however on most you will be charged YQ/YR.
Also note BA charges per segment except when booking two or more BA partners on one ticket.
LHR-DOH-BKK on BA/QR would be 120k avios in J one way for example, as it prices as two 60k J awards.
I believe AA will only allow routing Europe to Asia via Doha if both flights are with QR.
See also:
http://www.flyertalk.com/forum/briti...os-2016-a.html